Twin peaks kHz QPOs: mathematics of the 3:2 orbital resonance

Abstract

Using the method of multiple scales, one can derive an analytic solution that describes the behaviour of weakly coupled, non-linear oscillations in nearly Keplerian discs around neutron stars or black holes close to the 3:2 orbital epicyclic resonance. The solution obtained agrees with the previous numerical simulation. Such result may be relevant to the kilohertz quasi-periodic variability in X-ray fluxes observed in many Galactic black hole and neutron star sources. With a particular choice of tunable parameters, the solution fits accurately the observational data for Sco X-1.

Published (25 June 2004) on PASJ, 56, 553

References in corpus (4)

• Millisecond Oscillations in X-Ray Binaries
• Evidence for Harmonic Relationships in the High Frequency QPOs of XTE J1550-564 and GRO J1655-40
• Non-linear resonance in nearly geodesic motion in low-mass X-ray binaries
• Evidence for a 2:3 resonance in Sco X-1 kHz QPOs

Cited by in corpus (47)

• Foundations of Black Hole Accretion Disk Theory
• Confronting the models of 3:2 quasiperiodic oscillations with the rapid spin of the microquasar GRS 1915+105
• The distribution of kHz QPO frequencies in bright LMXBs
• Light Curves from an MHD Simulation of a Black Hole Accretion Disk
• On the kHz QPO frequency correlations in bright neutron star X-ray binaries
• The correlations between the twin kHz QPO frequencies of LMXBs
• Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations
• Testing Kerr Black Hole Mimickers with Quasi-Periodic Oscillations from GRO J1655-40
• A new model for QPOs in accreting black holes: application to the microquasar GRS 1915+105
• Quasi-periodic oscillations from the accretion disk around rotating traversable wormholes
• 2:3 Twin Quasi-Periodic Oscillations in Magnetohydrodynamic Accretion Flows
• Quasi-periodic Oscillations in Rotating Ellis Wormhole Spacetimes
• Studying Frequency Relations of kHz QPOs for 4U 1636-53 and Sco X-1: Observations Confront Theories
• Weak nonlinear coupling between epicyclic modes in slender tori
• Testing black holes in non-linear electrodynamics from the observed quasi-periodic oscillations
• Twin-peak quasiperiodic oscillations as an internal resonance
• An explanation for the kHz-QPO twin peaks separation in slow and fast rotators
• Looking for extra dimensions in the observed quasi-periodic oscillations of black holes
• Reversal of the amplitude difference of kHz QPOs in six atoll sources
• Internal resonance in non-linear disk oscillations and the amplitude evolution of neutron star kilohertz QPOs
• Of NBOs and kHz QPOs: a low-frequency modulation in resonant oscillations of relativistic accretion disks
• Oscillations of Thick Accretion Discs Around Black Holes
• On the parameters of the spherically symmetric parametrized Rezzolla-Zhidenko spacetime through solar system tests, orbit of S2 star about Sgr A${}^{\star }$, and quasiperiodic oscillations
• Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model
• High frequency QPOs: nonlinear oscillations in strong gravity
• Difficulties with the QPOs Resonance Model
• Oscillations of Thick Accretion Discs Around Black Holes - II
• Period doubling and non-linear resonance in the black hole candidate IGR J17091-3624 ?
• A Resonantly-Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars
• Deciphering signatures of Bardeen black holes from the observed quasi-periodic oscillations
• Mass of the active galactic nucleus black hole XMMUJ134736.6+173403
• Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars. II. Forced resonances
• The autoparametric 3:2 resonance in conservative systems
• The Interpretations For the Low and High Frequency QPO Correlations of X-ray Sources Among White Dwarfs, Neutron Stars and Black Holes
• Quasi-periodic oscillations from the accretion disk around distorted black holes
• Forced oscillations in a hydrodynamical accretion disk and QPOs
• Spin precession frequencies of a test gyroscope around a naked singularity and quasi-periodic oscillations
• Kinematic Density Waves in Accretion Disks
• Signatures of Einstein-Maxwell dilaton-axion gravity from the observed quasi-periodic oscillations in black holes
• Probing the nature of Einstein nonlinear Maxwell Yukawa black hole through gravitational wave forms from periodic orbits and quasiperiodic oscillations
• Constraining the rotating Simpson-Visser spacetime from the observed quasi-periodic oscillations in black holes
• Research on high-frequency quasi-periodic oscillations in black bounce-type spacetime
• Constraining the mass and moment of inertia of neutron stars from quasi-periodic oscillations in X-ray binaries
• Epicyclic oscillations and accretion disk around a special Buchdahl-inspired spacetime
• Observational constraints on the Kerr and its several single-parameter modified spacetimes using quasi-periodic oscillation data
• Resonance conditions
• QPOs: Einstein's gravity non-linear resonances